Beyond the
“simple”
recharge
paradigm
Axel
Timmermann
Is ENSO still interesting?
Citations per year
Source: Web of Science
title
abstract
Recap: ENSO recharge paradigm
Recap: ENSO recharge paradigm
Discharging, Sverdrup
Transport term
dhW
 rhW   bTE
dt
dTE
 RTE   hW
dt
R  c   b
+ Damping nonlinearity
Beyond the “simple” recharge paradigm
•
•
•
•
•
•
Nonlinearity, skewness and bursting
Annual-cycle ENSO coupling
Noise-induced instability
ENSO flavors
ENSO “diversity”
Response to external forcing
Reasons for ENSO skewness
Saddle node
1. Nonlinear SST equation
2. Nonlinear atmospheric response
-convection depends on total SST
-Interaction of ENSO with atmospheric noise
ENSO skewness and ENSO bursting
12oN
6 oN
0o
6 oS
12oS
150oE
180oW
150oW
120oW
1982-12 1000mb
90oW
ENSO skewness and ENSO bursting
Radiative conv.
Equilibrium state is
saddle point
Highly unstable
Period-doubling
Bifurcations generate
Chaos and low-frequency
Variability
There is a permanent
La Nina state for large
coupling
ENSO skewness and ENSO bursting
Error growth rate
strongly statedependent
Certain stretches on
attractor of well
Predictable
Possibility for regime
predictability
Nonlinear Atmospheric Response
S. Philip 2009
Wind response to quadratic SSTA
For a large El Nino, the warm pool and main convection center extend eastward,
enhanced westerly wind anomalies
For a large La Nina, the main convection zone shrinks
Weaker easterly wind response
With atmospheric nonlinearity
And state-dependent noise
Beyond the “simple” recharge paradigm
•
•
•
•
•
•
Nonlinearity, skewness and bursting
Annual-cycle ENSO coupling
Noise-induced instability
ENSO flavors
ENSO “diversity”
Response to external forcing
ENSO annual cycle interaction
Annual cycle
ENSO
PDO, IPO
MJO, WWB
Periodically modulated coupling of a linear
oscillator
Observations
γ(t) =γ0+α sin(ωat)
Recharge model
Amplitude
Modulation
Periodically forced NONLINEAR OSCILLATOR
produces….
K
Ω
Arnol’d Tongues
Periodically forced NONLINEAR OSCILLATOR
produces the Devil’s Staircase
Periodically forced NONLINEAR OSCILLATOR
produces the Devil’s Staircase
Periodically forced NONLINEAR OSCILLATOR
produces frequency entrainment
Stroboscopic view
ENSO amplitude
Dominant frequency
Annual cycle amplitude
Effect of AMOC
Shutdown on ENSO
Abrupt changes
of ENSO
Abrupt changes
of ENSO
Timmermann et al. (2007)
140,000-100,000 years ago
140,000-100,000 years ago
Orbital forcing effects on ENSO
Beyond the “simple” recharge paradigm
•
•
•
•
•
•
Nonlinearity, skewness and bursting
Annual-cycle ENSO coupling
Noise-induced instability
ENSO flavors
ENSO “diversity”
Response to external forcing
Noise-induced intensification of ENSO
Eisenman et al. 2005
WWB modulation by temperature for present-day climate
ENSO recharge model with state-dependent
noise
dT
dt
dh
dt
d
dt
  T
  h   (t)G,
PDFT
0.07
0.06
  T
 a (t)G,
0.05
0.04
B=0
0.03
B=1
0.02
 r  w(t) .
G 1 BT
0.01
0
-2
-1
0
1
2
3
Coupling strength and noise may change slowly
over time
ENSO recharge model with state-dependent
noise
Ensemble mean equation for ENSO
d T 
dt
  E  T    h   B / (r     / r) ,
2
2
dh
dt
   T 
E     B / (r     / r)
2
2
2
State-dependent noise is “coupling”
State-dependent noise is also “nonlinearity”
ENSO recharge model with state-dependent
noise
dT
dt
dh
dt
d
dt
  T
  h   (t)G,
PDFT
0.07
0.06
  T
 a (t)G,
0.05
0.04
B=0
0.03
B=1
0.02
 r  w(t) .
G 1 BT
0.01
0
-2
-1
0
1
2
3
Coupling strength and noise may change slowly
over time
ENSO recharge model with state-dependent
noise
Ensemble mean equation for ENSO
d T 
dt
  E  T    h   B / (r     / r) ,
2
2
dh
dt
   T 
E     B / (r     / r)
2
2
2
State-dependent noise is “coupling”
State-dependent noise is also “nonlinearity”
ENSO recharge model with state-dependent
noise
Ensemble variance equation for ENSO
1 d  T '2 
2
2
    T '    h 'T '    T '   B  T ' 
2
dt
1 d  h '2 
   h 'T ' 
2
dt
d  h 'T ' 
dt
 
 h 'T '   ( h '2    T '2 )    h '   B  h 'T ' 
Deriving third order equations and 4th
Order closure
  2T 2  2   2T 2  2  T 2 ,   2hT   2   2  hT   2  hT  
We can obtain a closed set of equations for the ensemble variance
ENSO recharge model with state-dependent
noise
period
d  T '2 
 2  T '2  2  h'T ' 
dt
 2 (1  B  T )  T '  2B  T '2 
Teast
period/2
d  h'2 
 2  h'T '  2a (1  B  T )  h' 
dt
 2aB  h'T ' 
Temperature variance
Time [months]
Instability of the second order moments is
associated with error dynamics
Beyond the “simple” recharge paradigm
•
•
•
•
•
•
Nonlinearity, skewness and bursting
Annual-cycle ENSO coupling
Noise-induced instability
ENSO flavors
ENSO “diversity”
Response to external forcing
Multiplicity of ENSO modes
Westward-propagating SST mode
Interannual mode
Quasi-biennial mode
Warm-pool El Nino, Modoki
The SST mode
Consider a simple case:
Ocean mean current is at rest:
u1  v1  w  0
Mean SST is constant, then the SST equation
r
r
t T '  u T ' u1' T  w(T '  h) / H1  w'(T  Tsub ) / H1  T '
1
becomes:
Tsub
)/ H
 T
'
ttTT ''  w'(T
w '(T 
Tsub
) /1 H
1  T '
  Au
w  
 2 ua
T '
2
C
  ua  a
x 2
x
'
x
H2
H
 /
2
s
x
2
a
a
a T '
—  ua  2
 x
Simplified Gill solution
The SST mode equation
T '
t T '  w '(T  Tsub ) / H1   T '  b
 T '
x
H2 a
b
HH1  2


2
2
s s
(T  Tsub )
A westward propagating
SST mode!
Note the zonal T derivative originates
From the wind stress, not directly from
The zonal advection.
The Thermocline mode
Ignore ocean current anomalies
r
r
t T '  u T ' u1' T  w(T '  h) / H1  w'(T  Tsub ) / H1  T '
1
t T '  w(T '  h) / H1  T '   W h  W T '

x
aa H a T '
 a H aua 

x
Simplified Gill solution: K-wave
 u   yv  g  h   u   /  H
 yu  g  h
 h  H ( u   v)   h
'
t
m
m
x
'
m
t
 
x
aa H a T '
y
y
m
x
Reduced gravity equations
The mixed mode
The Mixed-Thermocline
mode
Cold tongue versus warm pool El Nino
EOF2, Timmermann 2001
EOF2, Timmermann 2003
Dateline El Nino, Larkin and Harrison 2005
El Nino Modoki, Ashok et al. 2007
Central Pacific El Nino, Kao and Yu 2009
Warm Pool El Nino, Kug et al. 2009
SST and precipitation
El Nino flavors and their impact on Australia
EOF2 of SSTA, Timmermann et al. 2003
ColdModoki
tongue El Nino
drought
DJF
MAM
JJA
Courtesy of Harry Hendon
SON
El Nino flavors and their impact on Australia
EOF2 of SSTA, Timmermann et al. 2003
Modoki
Explains why the rainfall response to the El Nino 1997/98 was relatively weak in Australia
drought
DJF
MAM
JJA
Courtesy of Harry Hendon
SON
Beyond the “simple” recharge paradigm
•
•
•
•
•
•
Nonlinearity, skewness and bursting
Annual-cycle ENSO coupling
Noise-induced instability
ENSO flavors
ENSO complexity
Response to external forcing
ENSO complexity
From Slingo
What controls the amplitude of ENSO?
Noise level
dT/dt=f (T,u..)+Σ(T)ζ
Strength of annual
cycle
dT/dt=f (T,u..)+Asinωt
ENSO variance
maybe skewness
Background state
dT/dt=f (T,u,h,v,w)
External factors
Nonlinearities
dT/dt=f (u'T', Σ(T)ζ)
Beyond the “simple” recharge paradigm
•
•
•
•
•
•
Nonlinearity, skewness and bursting
Annual-cycle ENSO coupling
Noise-induced instability
ENSO flavors
ENSO “diversity”
Response to external forcing
Projected climate change versus model bias
Many state-of-the-art
coupled general circulation
models still suffer from
biases in the mean and the
annual cycle
+2C
Enhanced equatorial
warming pattern, dominant
climate response in the
tropical Pacific
-2C
2-4C
SST model bias
SST model bias in a “typical” state-of-the-art climate model
ENSO performance in climate models
Standard deviation
of sea surface
Temperature
anomalies
Guilyardi et al. 2009
Future Changes of ENSO, AR4
“All IPCC AR4 models show continued ENSO interannual variability in the future
no matter what the change in average background conditions, but changes in
ENSO interannual variability differ from model to model.” , IPCC AR4
ENSO change 2100
Yamaguchi and Noda
Noise-induced intensification of ENSO
AR4 models
simulate increased
Intraseasonal
variability
WWB-ENSO interaction
increased during the
last 50 years
Conclusions
TODAY
IN THE FUTURE